Question 784598


{{{g(x)=x/(x^2-16 )  }}} 

since {{{(x^2-16 )  }}} is denominator, domain will be all real numbers {{{x}}} except value of {{{x}}} that makes denominator equal to zero and these are:

{{{(x^2-16 )=0  }}}....factor completely

{{{(x^2-4^2)=0  }}}

{{{(x-4)(x+4)=0  }}}

if 
{{{(x-4)=0  }}}=> {{{x=4}}}

or
if 
{{{(x+4)=0  }}}=> {{{x=-4}}}

so, vertical asymptotes are: {{{x=4}}} and {{{x=-4}}}


{{{drawing(600,600,   -10, 10, -10, 10,  blue(line(-4,10,-4,-10)), blue(line(4,10,4,-10)),grid(0),
graph(600,600,   -10, 10, -10, 10,x/(x^2-16 ))) }}}